Mathematician, astronomer, physician, and lawyer
Born: c. 390 b. c.e.; Cnidus, Asia Minor (now in Turkey)
Died: c. 337 b. c.e.; Cnidus, Asia Minor (now in Turkey)
Category: Mathematics; astronomy and cosmology; medicine; law
Life Eudoxus of Cnidus (yew-DAHK-suhs of NI-duhs) studied mathematics with Archytas in Tarentum and in Athens under Plato. Later, he founded a school in Cyzicus. Eudoxus made two main mathematical contributions: expanding the application for an area-finding method and creating a new theory of incommensurables. First, he took Antiphon’s “method of exhaustion,” used to find the area of a circle, and proved that it could be applied to finding the areas and volumes of other figures. This method “exhausts” the area inside an unknown figure by inscribing multiple figures with known areas inside it. Second, he solved a problem created by Greek mathematics’ conception of numbers as lengths of lines. This idea works well for rational numbers but encounters difficulty with irrational numbers. As a solution, Eudoxus created the theory of incommensurables. This is the subject of book 5 of Euclid’s Stoicheia (compiled c. 300 b. c.e.; Elements, 1570), probably written by Eudoxus.
In astronomy, Eudoxus calculated the circumference of the earth, reported by Aristotle to be 40,000 miles (64,400 kilometers). Eudoxus also originated a theory that the complex movement through the sky of the Sun, Moon, planets, and stars is dependent on their positions on rotating concentric celestial spheres.
Influence Eudoxus’s method of exhaustion presaged integral calculus by almost two thousand years. His theory of incommensurables foreshadowed the nineteenth century formulation of the real numbers by German mathematicians Julius Wilhelm Richard Dedekind and Karl Theodor Wilhelm Weierstrass. His celestial sphere theory was held as the true description of the universe until the rise of the heliocentric theory during the Renaissance.
Eudoxus of Cnidus Further Reading
Euclid. The Elements, Book V. Translated by Sir Thomas Heath. New York: Dover, 1956.
Lindberg, David. The Beginnings of Western Science. Chicago: University of Chicago Press, 1992.
Linton, C. M. From Eudoxus to Einstein: A History of Mathematical Astronomy. New York: Cambridge University Press, 2004.
Smith, D. E. History of Mathematics. New York: Dover, 1951.
Andrius Tamulis
See also: Antiphon; Archytas of Tartenum; Euclid; Plato; Science.
World History
